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Full text of "IS 15431: Seven Basic Tools for Quality Management"

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Disclosure to Promote the Right To Information 

Whereas the Parliament of India has set out to provide a practical regime of right to 
information for citizens to secure access to information under the control of public authorities, 
in order to promote transparency and accountability in the working of every public authority, 
and whereas the attached publication of the Bureau of Indian Standards is of particular interest 
to the public, particularly disadvantaged communities and those engaged in the pursuit of 
education and knowledge, the attached public safety standard is made available to promote the 
timely dissemination of this information in an accurate manner to the public. 

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Jawaharlal Nehru 

Step Out From the Old to the New 



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PROTECTED BY COPYRIGHT 



IS 15431 :2003 

7ju[cn yeRT ^ fen? ^^trt ^ ^x[^f>y^ 

Indian Standard 
SEVEN BASIC TOOLS FOR QUALITY MANAGEMENT 



ICS 03.120.30 



© BIS 2003 

BUREAU OF INDIAN STANDARDS 

MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG 
NEW DELHI 110002 



December 2003 Price Group 8 



Statistical Methods for Quality and Reliability Sectional Committee, MSD 3 



FOREWORD 

This Indian Standard was adopted by the Bureau of Indian Standards, after the draft finalized by the Statistical 
Methods for Quality and Reliability Sectional Committee, had been approved by the Management and Systems 
Division Council. 

In the backdrop of globalization of market economy, quality at a competitive price has become the most important 
consideration in customer's selection of a product or service. Quality, in fact, has become the key factor in all 
types of industries — manufacturing, process, service and software. To ensure fullest possible satisfaction of the 
customer, the manufacturer or the service provider has to have a total approach for achieving a twin goal: on the 
one hand, to ensure quality of products/services through market survey on customers needs and expectations, 
translating these into various features and characteristics with defined acceptability criteria, fulfilling these at all 
stages of manufacture by adopting quality control and quality improvement techniques, proper marketing and 
ensuring prompt and adequate after-sales service; on the other, reduction of cost due to scrap, rework, return, 
warranty claims etc, which affect quality. 

To achieve the twin goal, a system has to be introduced which takes care of not only correction of quality 
deficiencies as and when they occur but also their prevention through planned efforts for continuous improvement 
in quality, waste elimination, maintenance and calibration of equipment's, education and training of staff, etc. 

In solving a quality problem, Deming's Plan-Do-Check-Act (PDCA) cycle is worth following. At the 'Plan' 
stage, one has to select the problem to be solved, schedule the activities, understand the current situation, set the 
target, analyze the problem and plan counter measures. At the 'Do' stage, one has to implement the plan. At the 
'Check' stage, resuhs achieved are to be checked to see if plans were executed as expected, and objectives were 
achieved as planned. At the 'Act' stage, if the objectives are not met, one has to analyze the results further and 
plan counter measures; if objectives are met one has to formalize and standardize measures adopted. At this 
stage, the whole exercise is to be reviewed and measures for further improvements are to be planned. 




For understanding and solving a quality problem towards achieving the above twin goal, the essential approach 
is to study the pattern of variation in the pertinent area and properly measure this variation. Several simple and 
basic tools are available for systematically studying the pattern of variation in solving a quality problem, and 
thereby ultimately achieving quality improvement and cost reduction. These tools are: 

a) Cause and effect diagram 

b) Check sheet 

c) Pareto diagram 

d) Histogram 

c) Stratification 

f) Run chart 

g) Scatter diagram 

The above seven tools, are essentially simple seven tools of Statistical Process Control (SPC). These tools are 
simple to learn irrespective of the background of the learners, easy to apply, inexpensive, and yet produce abundant 
returns. Any sincere effort in an industry to solve a quality problem, and thereby quality improvement and cost 
reduction must start with introduction of training in and use of these tools. 

The composition of the Committee responsible for the formulation of this standard is given in Annex A. 



IS 15431 : 2003 



Indian Standard 
SEVEN BASIC TOOLS FOR QUALITY MANAGEMENT 



1 SCOPE 

This standard describes the following seven basic tools 
for quality management: 



a) 


Cause and effect dia 


gram 


b) 


Check sheet 




c) 


Pareto diagram 




d) 


Histogram 




e) 


Stratification 




f) 


Run chart 




g) 


Scatter diagram 





The above tools have been illustrated with the examples 
for better understanding. 

2 REFERENCES 

The following standards contain provisions, which 
through reference in this text constitute provisions of 
this standard. At the time of publication, the editions 
indicated were valid. All standards are subject to 
revision and parties to agreements based on this 
standard are encouraged to investigate the possibility 
of applying the most recent editions of the standards 
indicated below: 

IS No. Title 

397 (Part 1 ) : Method for statistical quality control 

2003 during production : Part 1 Control 

charts for variables {second revision) 

7300 : 2003 Methods of regression and 

correlation {second revision) 
12801:1989 Pareto diagram and cause and effect 

diagram 

3 TERMINOLOGY 

3.1 Cause and Effect Diagram — Cause and effect 
diagram lists out in a classified and systematic manner 
all the variables, which are responsible for a problem 
or condition. It provides a method of exploring, 
identifying, classifying, organizing and displaying 
potential causes of a problem to discover its root causes, 
with a view to solving the problem at hand, and 
achieving improvement in quality in the long run. 

NOTE — This tool was developed by Dr K. Ishikawa in Japan. 
This is also known as Ishikawa Diagram or Fish-bone Diagram 
(because of its shape). 

3.2 Check Sheet — A check sheet is a template for 
systematic and easy way of recording the data from 



historical sources or observations for understanding 
the status, analysis, monitoring and for decision- 
making. Check sheets are for counting and 
accumulating data so that patterns and trends can be 
clearly detected and shown. 

3.3 Pareto Diagram — A pareto diagram is a simple 
graphical technique for ranking items from the most 
frequent to the least frequent. This diagram displays 
in decreasing order, the relative contribution of each 
item to the total effect. The relative contribution may 
be based on the number of occurrences, the cost 
associated with each item, or other measures of impact 
on the effect. Bars are used to show the relative 
contribution of each item. A cumulative frequency 
line is used to show the cumulative contribution of 
items. 

3.4 Histogram — A histogram may be defined as a 
graphical-cum-pictorial presentation of variation of a 
single parameter observed in a set of data emerging 
from any process. It consists of series of rectangles 
with the range of variate as base and height 
proportional to corresponding frequency. 

3.5 Stratification — Stratification may be defined as 
the process of classifying data into groups such that 
data within groups are as much homogenous as 
possible, while data between groups are possibly 
heterogeneous, so that intra-stratum variation is low, 
but inter-strata variation is high. 

3.6 Run Chart — Run chart is a graphical presentation 
of data with time-scale on horizontal axis. It is a simple 
means of displaying trends, cycles, shifts etc, in a 
variable within observation points over a specified 
time-period, 

3.7 Scatter Diagram - — In the present context — for 
every quality parameter of interest, there is need to 
assess the nature and/or degree of impact on output of 
resulting 'quality parameter' as reflected in the 
observed changes caused by corresponding variations 
in the 'input parameter'. The former is called 
dependent variable and the latter independent variable. 
Attempts are made to get the behaviour of dependent 
variable in desired range by monitoring the 
independent variable in appropriately determined limits 
as indicated by the nature of relationship between the 
two. The dependent variable is plotted along j^-axis 
and the independent along ;t-axis. Such a diagram is 
called a scatter diagram. 



IS 15431 : 2003 



4 CAUSE AND EFFECT DIAGRAM 

4.1 General 

A cause and effect diagram is a diagrammatic 
representation of the relationship between a given 
effect (a quality problem, for example, variation in a 
quality characteristics), shown as the backbone, and 
its potential secondary and tertiary causes shown as 
the bones and sub-bones, grouped under major 
categories and sub-categories, respectively, so that the 
diagram looks like the skeleton of a fish. The diagram 
is often constructed by groups, but it may be 
constructed by individuals possessing appropriate 
process knowledge and experience. 

4.2 Scope 

It is a mapping technique for problems in areas like 
rejection/rework, warranty complaints, accidents, 
productivity and administration. A cause and effect 
diagram is used for analyzing and communicating 
cause-effect relationships in any of the above areas, 
and thereby facilitating solution of the problem by 
tracing the route; symptoms-causes-solution. 

4.3 Steps for Construction 

4.3.1 Define the effect (problem) that is to be diagnosed 
and solved clearly and concisely. Draw a broad arrow 
(the backbone) from the left to the right and indicate 
the problem on the right-hand side. 

4.3.2 Organize a brainstorming session involving 
everyone connected with the problem (for example, 
production operators, supervisors, engineers, and 
others who can contribute in identifying the causes). 
For the success of a brainstorming session, it has to be 
ensured that all participants are encouraged to suggest 
ideas. All suggested causes and opinions, however, 
mundane, should be noted/listed without criticism. 

NOTE — Brainstorming is a common metiiod for a team to 
creatively and efficiently generate high volume of ideas on any 
topic by creating a process that is free of criticism and judgement. 

4.3.3 Identify the major categories of possible causes 
from the 'Brainstormed' list of potential causes of any 
effect into several relevant classes which may include: 



a) 


Men, 


b) 


Machines, 


c) 


Materials, 


d) 


Methods, 


e) 


Measurement, 





Environment, and 


g) 


Data and information systems 



4.3.4 Begin to construct the diagram, defining the effect 
in a box on the right-hand side and positioning major 
categories as feeders to the Effect box (see Fig. 1). 

4.3.5 For each main cause, define and list any sub cause 
(level 2) that may contribute to the problems against 
the small arrows coming out from main causes 
{see Fig. 2). This process of sub-division is carried on 
until all causes listed are accommodated. A well- 
developed diagram will have no branches of less than 
two levels, and many with three or more levels. 

4.3.6 Once constructed, the diagram can become a 
living tool with further refinements being introduced 
as new knowledge and experience are gained. 

4.4 Types of Cause and Effect Diagrams 

4.4.1 Most widely used types of cause and effect 
diagrams are given below. 

4.4.1.1 Dispersion analysis type 

It is constructed by placing individual causes within 
each major cause category and asking 'Why does this 
cause happen?' for each item. 

4.4.1.2 Process classification type 

It sequentially lists all the steps in a process. The same 
cause category arrows as in the dispersion analysis type 
branch off line between each process step. The same 
questions are then applied to each cause category as in 
the dispersion analysis type diagram. 

4.4.1.3 Cause enumeration type 

It is almost identical to the dispersion analysis type. The 
only real difference rests in the fact that cause enumeration 
first organizes all the possible causes in list form and then 
places them in the major cause categories. 



Category 




Category 



Category 



Effect 



Category 



Fig. 1 Basic Structure of Cause and Effect Diagram 



IS 15431 :2003 




Level 2 Cause 



Level 1 Cause 



Level 3 Cause 





Effect 



Fig. 2 Development of Cause and Effect Diagram 



4.5 Uses 

4.5.1 Cause and effect diagrams are most useful in 
group problem solving situations. In themselves they 
do not provide any solutions. However, the process 
by which they are constructed is enlightening and 
promotes better understanding of the problem by all 
concerned. Even people who do not yet know a great 
deal about their jobs can learn a lot from making a 
cause and effect diagram or merely studying a 
completed one. 

4.5.2 Straying from the topics and repetition of 
complaints and grievances is avoided since a cause 
and effect diagram serves as a focus for the discussion. 
This is because every one knows the topic and the 
discussions so far advanced. The conclusion on actions 
to be taken may also be reached faster. 

4.5.3 A cause and effect diagram shows the level of 
ability of the group responsible for drawing it. 

4.5.4 The cause and effect diagram permits viewing 
the variables in perspective and in relation to each other 
with resulting improvement through planning. 

4.5.5 The use of cause and effect diagrams helps to 
unify and systematize the thoughts of the team. 

4.6 Example 

An example of cause and effect diagram to find reasons 
for 'Poor Quality Photocopying' is given in Fig. 3. 

5 CHECK SHEET 
5.1 General 

A good quality control programme aims primarily at 



prevention of non-conformities. It requires generation 
of data on output parameter{s) and the corresponding 
input parameters. The data thus generated are used to 
assess whether what is being done is as required or 
planned. Therefore the purpose for which the data are 
being collected must be clear. If the data collected are 
inaccurate, even, the best statistical tool employed for 
their analysis will only result in drawing wrong 
conclusions. 

5.2 Scope 

Check sheets can be used in various areas like customer 
complaints, lost production time, machine failures, 
appearance rejects, leakages, non-conformities, 
accidents and clerical errors. 

5.3 Steps for Construction 

Steps for construction of a check sheet may be 
enumerated as follows: 

a) Agree on the definitions of the events or 
conditions being observed. 

b) Clarify the purpose for collection of data. 

c) Determine the time period for collection of 
data. 

d) Decide on variety of information that must 
be collected. 

e) Stratify the information as much as possible. 
It can be done area-wise, zone-wise, shift- 
wise, machine-wise, supplier-wise, operator- 
wise etc. 

f) Design the proper format that will facilitate 
the collection of needed data (clear, complete 
and easy to use). 



IS 15431 : 2003 

Method 



Materials 



Handling 



Original setting 

Drying \ Degree of 
time ►y misalignment 



Dirtiness 




Transparenc; 
Paper quality 
Strengt] 

Curl 
Dirtiness of table 




Storage period\^ 
Newness 



H^dness of pencil 

Speed 
Sharpness 

Writing pressure 

Dirtiness of lens 

Brightness of lamp 

Operating hours 




Paper 
quality A 



Storage period 

Degree of 
exposure 



Storage 
method 




Poor quality 
photocopying 



Condition of call 



Materials 



Machine 



Causes Effect 

Fig. 3 Example of Cause and Effect Diagram for Poor Quality Photocopying 



g) Record the data on the check sheet so 
designed. Collect the data consistently and 
accurately. Above all act on the data as 
quickly as possible. 

5,4 Types of Check Sheets 

The various types of check sheets normally used are 
as follows: 

a) Production process distribution check sheet, 
for recording data on physical measurement 
of quality characteristics. 

b) Non-conforming cause-wise check sheet, for 
recording frequencies of various causes of 
non-conformity. 

c) Non-conformity location check sheet, for 
identifying arrears of occurrence of a 



particular non-conformity, for example, 
bubbles in an item made of glass. 

d) Check sheet for tracing sources of causes of 
non-conformity, for example, according to 
man, machine days, shift, etc. 

e) Check up confirmation check sheet, for 
example, those used for quality audit. 

5.5 Uses 

5.5.1 The two general uses of check sheets for data 
collection are for process control and problem analysis. 
It makes the patterns in the data obvious quickly. 

5.5.2 Use in Process Control 

Every work process has a number of indicators on how 
the process is performing. All types of check sheets 
can be used to collect information on key indicators. 



IS 15431 :2003 



Collection and later analysis of this information is an 
important part of monitoring a process. 

5.5.3 Use in Problem Analysis 

Check sheets can be used to answer who, what, where, 
when, why and how many times while determining 
the root cause of a problem during trouble shooting. 
Also check sheets are utilized to verify that a problem 
has been solved when a root cause has been eliminated. 

5.6 Examples 

Two examples of Check Sheets are given in Table 1 
and Table 2. 

6 PARETO DIAGRAM 

6.1 General 

Pareto diagram is a method of prioritizing/identifying 
the most critical problems. It is usually used in 
conjunction with cause and effect diagram in order to 
determining which items contribute most to a particular 
effect. This technique is named after an Italian 
Economist, Vilfredo Pareto, who was the first to 
observe that in any country the lion's share (70-90 
percent) of total national wealth was owned by a few 
{10-20 percent) rich people. Thereafter it has been 
observed in terms of quality that a large percentage of 
problems are because of a small percentage of items. 
Pareto diagram identifies these 'vital few' items 
{from 'trivial many') so as to first take action on them 
first. 

6.2 Scope 

The tool may be used in areas like rejection, delivery, 
rework, complaints, accidents, administration, costing, 
efficiency, conservation of materials and energy. 



6.3 Steps for Construction 

6.3.1 The Pareto diagram may be 'cause-wise', such 
as, different operators, different machines, raw 
material, etc, or they may be 'effect-wise' such as 
number of non-conformities, non-conforming items, 
faults, complaints, repairs, accidents, default in 
payments, delay and loss expenses. Often a Pareto 
diagram of 'Effect' is constructed first, then a cause- 
and-effect diagram is used to find from the principal 
effect(s) the probable causes, which is again studied 
with another Pareto diagram for identifying the vital 
items. 

6.3.2 The steps for construction of a Pareto diagram 
may be enumerated as follows: 

a) Decide on how the data should be classified, 
for example, shift-wise, according to types of 
non-conformity, etc. 

b) Select the items to be analyzed. 

c) Prepare a suitable check-sheet for collection 
of data, selecting the unit of measurement for 
analysis. 

d) Choose the time period for collection of data. 
Try to keep the time period the same for all 
related Pareto diagrams to facilitate 
comparison in future. 

e) For each cause effect, obtain the frequency 
of occurrences. 

f) Draw horizontal and vertical axis on a graph 
paper. 

g) Divide horizontal axis into equal segments, 
one for each cause/effect. Scale the vertical 
axis in such a way that the top of the axis 
represents a number equal to the sum of the 
frequencies for all the causes/effects. 



Table 1 Non-conforming Cause-Wise Check Sheet 

{Clause -5. 6) 



Product; 

Manufacturing stage: Final inspection 

Type of non-conformity: Scar, incomplete, mis-shapen 

Total No. inspected: 2530 



Date: 
Factory: 
Section: 

Inspector's name: 
Lot No. 
Order No. 



Type 



Tally Marks 



Sub-Total 



Surface scar 


;/// //// /;y; hjj jjjj jjji ii 
tTTT III! tTTTtTTT TnTTTTT ft 


Cracks 


mmmmiii 


Incomplete 


Itll lilt Ifti iHi iiii itil mi III! JiH III 

TnTTTuTiTT TTn TnT TuT TfiT TuT TTTT III 


Mis-shapen 


nil 


Others 


mm 



32 

23 

48 

4 



Total NCs: 



115 



Total Rejects 



! ! ! ! f'r' 'I'f i tit ' ' ' ' t !t ' ' 1 1 f ' t ! I ' ' ' ' ' ' " " ' ' "' ' I "I '>'> nil nil ml I 

Tttt mt mr tm Tut Tm tttt fm tttt IIII IIII IIII IIII I If I It ft titt fttt I 



86 



IS 15431 : 2003 



Table 2 Check Sheet for Tracing Sources of Cause of Non-conformity 

(Clause 5.6) 



Equipment 


Worker 


Monday 


Tuesday 


Wednesday 


Thursday 


Friday 


Saturday 




FN 


AN 


FN 


AN 


FN 


AN 


FN 


AN 


FN 


AN 


FN 


AN 


Machine 1 




O 


o e 


O 


o e 


O 


o o 


O 


o e 


O 


O 


O 


mc, 






o e 




O 


e 


O 


o o 


O 


e 


O 


o 












o 




o e 


eee 


o 




O 










A 


; 








ee? 




o 

e q 




O 












o 


o 


o 


o 


o 


oo 





o 


o 


o 





60^ 








o 


o 


o 


o 


oo 





o 


Oe 


o 












o 


Oe 


o 


oo 


o 


Oe 


? 


o 








B 




o 
o 


o 
o 

oe 
e 


e 


o 
o 

Oe 
e 




o 



e 


?<; 




o 
o 






Machine 2 


C 


o 

o e 


o e 


o 
o 


I 


o 
o 
o 
o 
o 


o o 




? 


M 


o 





o 




D 


e 


e 




<i 


<;ii 


e 




n 


nn° 


« 


°e 


ee° 



O : Surface Scratch, c, : Improper Shape, e: Blow Hole, ° : Others, n : Poor Finishing. 



h) Write the cause/effect with maximum 
frequency at the left hand side of the 
horizontal axis followed by second maximum 
frequency and so on. The 'others' group is 
to be plotted at the extreme right hand side 
irrespective of its frequency. 

j) For each cause/effect, draw a bar. The height 
of bar shows the frequency of occurrence. 
Keep width of bars the same and each one 
should be in contact with its adjacent bar. 

k) Plot a line graph for the cumulative 
percentages showing the portion of the total 
that cause/effect category represents. 

m) Construct another vertical axis on the right 
hand side of the graph and scale it from to 
1 00 percent. The termination of the cumulative 
line should be at the point marked 100 percent. 
This 100 percent point shall correspond to the 
sum of the frequencies for all the causes, 

n) Add suitable legend and write briefly the source 
of data and any other relevant information. 

p) Interpret the results. Generally the tallest 
bar indicates the biggest contributor to the 
overall problem. Ask: Which one has the 
most impact on the goals of the business and/ 
or customers. 

6.4 Uses 

6.4.1 It has been observed that different people in any 



organization try to make improvements individually 
without any definite basis for their efforts. This results 
in waste of lot of energy producing very few results. 
The Pareto diagram is an indispensable tool for 
knowing exactly where the collective efforts for 
improvement should be concentrated so as to have the 
maximum gains. It is more useful to reduce the tallest 
bar — the items for which quality problems occur most 
frequently by half, than to reduce a short bar to zero. 
To reduce the non-conforming items represented by 
short bar to zero, would require a tremendous effort 
since there are more or less inevitable non-conforming 
items occurring now and then. 

6.4.2 Pareto diagram can be applied for improvement 
in all aspects. In an organization, apart from the 
improvement of quality, there are many other 
problems, like efficiency, conservation of materials and 
energies, reduction in costs, safety and others. 
Whatever be the problem, Pareto diagram is the first 
step for improvement. 

6.4.3 Pareto diagram can also be used to confirm the 
impact of improvement. If effective measures have 
been taken, the order of the sources/causes on the 
horizontal axis will usually shift. Comparing the before 
and after improvement diagrams, if it is found that the 
first most important cause of the problem has dropped 
to second or may be third or fourth place on the 
horizontal axis and the first place has been taken by 



IS 15431 :2003 



the previous second biggest cause, this shows that 
effective measures have been taken and bigger the shift 
in the order the bigger the impact. 

6.5 Remarks 

6.5.1 When the vital few have been successfully 
contained on routine basis, it is time to repeat the Pareto 
diagram study. The causes which were not dominant 
hitherto, now become vital and need to be attended on 
priority. This journey continues. If at any stage one 
feels that 'zero non-conformity' has been achieved, 
the competition brings in new concept of quality (may 
be life, cost, reliability, new features) that once again 
shows prevalence of 'non-conformities' needing 
attention. Thus the journey continues. 

6.5.2 Sometimes it so happens that monetary loss 
resulting from a particular type of non-conformity is 
many times more than the loss resulting from some 



other type of non-conformity. In such a situation Pareto 
diagram should be based on proportion to the damage 
caused by non-conformities instead of usual proportion 
to the frequency of their occurrences. 

6.6 Examples 

6.6.1 Pareto Diagram for Rejection of Castings {See 
Table 3) 

6.6.2 Pareto Diagrams for Process Non-conformities 
— Before and After Improvement {See Table 4) 

6.6.2.1 On the basis of before improvement Pareto 
diagram on the left, the problem of improper rotation 
was selected for improvement. Comparing the before 
improvement and after improvement graphs it can be 
seen that improper rotation dropped to the second most 
important source of trouble, the first place being taken 
by the previous source, noise. 



Table 3 Details of Rejection of Castings 

{Clause 6.6.1) 



SI No. 

(1) 


Causes 

(2) 


Weight of Rejected 
Material (in kg) 

(3) 


Percent of Rejected 
Material 

(4) 


Cumulative Total in 
Percent 

(5) 



i) 


Blow hole 


ii) 


Shrinkage 


iii) 


Sand inclusion 


iv) 


Shift 


V) 


Mis-run 


vi) 


Slag inclusion 


vii) 


Incorrect dimension 


viii) 


Cold shot 


ix) 


Damages 


X) 


Others 



32.3 

27.4 

14.3 

10.1 

6.2 

4.4 

4.0 

2.0 

1.3 

5.0 



30.2 
25.6 
13.4 
9.4 
5,8 
4.1 
3.7 
1.9 
1.2 
4.7 



30.2 
55.8 
69.2 
78.6 
84.4 
88.5 
92.2 
94.1 
95.3 
100.0 



Total 



107.0 





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80- 


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□1 








^ 
















■ 


■70 


.^ 








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c 


60- 


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-60 








M 




















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20- 


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t= 






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Fig. 4 Pareto Diagram 



IS 15431 : 2003 



Table 4 Process of Non-conformities 

(Clause 6.6.2) 







Daia 


Before Improvement 




Data After Improvement 


SI 


Causes 




Non- 


Percent Non- 


Cum. Total 


Causes 


Non- 


Percent Non- 


< 
Cum. Total 


No. 






conforming 


conforming 


in 




conforming 


conforming 


in Percent 








Cases 


Cases 


Percent 




Cases 


Cases 




(1) 


(2) 




(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 




Improper rotation 


46 


39,0 


39.0 


Noise 


15 


24.6 


24.6 


ii) 


Noise 




18 


15.3 


54.3 


Improper rotation 


12 


19.7 


44.3 


iii) 


Wobble 




16 


13.6 


67.9 


Pressure 


11 


18.0 


62.3 


iv) 


Pressure 




14 


11.9 


79.8 


Wobble 


8 


13.1 


75.4 


v) 


Leftover 




11 


9.3 


89.1 


Axis Caulking 


7 


11.5 


86.9 


vi) 


Case Wobble 




4 


3.4 


92.5 


Case Wobble 


3 


4.9 


91.8 


vii) 


Others 




9 


7.5 


100.0 


Others 


5 


8.2 


100.0 




Total 




118 


100.0 




Total 


61 


100.0 







Before Improvement 






.80. 


- 




r 120 








(A 
TO 
U 




-^ 


- 100 c 


o>60 - 


j^— — ^'^^ 




o 


c 


j^-"""'^ 




- 80 = 


E 


^^^^y"^ 




n 


•2 40- 
o 




y^^ 




-60 .2 
Q 

•** 


c 


■^ifH 






-40 g 


^ 20 ■ 
o 


•^ ^ ^ ^ ^ 








-20 £ 


ll^lf; 






^l^ll 




TTtPA' 


i oJ 


:^|^|^ 


mil; 


^yl^ 








S $ ^ $ $ ■ 


■0 


C 03 03 m ,_ 03 


(A 




rotatio 
Nois 
WobbI 
ressur 
eftove 
Wobb 


03 

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1 " i 

S o 








Q. 








E 















After Improvement 




80-1 


r 1 


r200 


I 




■ 175 


(0 


t 




» 60- 


Overall effect - 

4 


■ 150 g 


c 


■ ■'25 i 


1 40- 
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z 20- 


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$5^55 


iiSSJJ 


ISSJ;;; 


■ $ ^ $ $ 


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L 




0) C m 03 n> 03 tn 


ois 
atio 
sur 
bbl 
kin 
bb 
her 




N 

proper rot 

Pres 

Wo 

Axle cau 

Case Wc 

Ot 






E 









Fig. 5 Pareto Diagram 



7 HISTOGRAM 

7.1 Scope 

The tool can be used for assessing the current process 
state, analyzing process variation, checking effective- 
ness of an improvement, etc. The most important use 
of the tool is for summarizing data frorti a process that 
have been collected over a period of time. 

7.2 Construction 

The following steps are to be taken for constructing a 

histogram: 

a) The total number of observations (on the 
quality characteristics of interest) should not 
be less (preferably more) than 100 so that 



frequency table may show any definite 
pattern, 

b) The class intervals should be of equal width 
for better graphical representation and easier 
computation of the mean, standard deviation, 
etc. 

c) Range (/?) of the data is calculated (the 
difference of the maximum and the minimum 
values). 

d) The total number of class intervals (K) in a 
frequency table should be between 7 and 15. 
It is because if the number of class intervals 
is too less there would be considerable 
error in further calculations, and if the number 
is too large it would result in many class 



IS 15431 :2003 



intervals having zero or very less frequencies. 

e) Having known the Range (/?) and that number 
of class intervals should be between 7 and 15, 
the class width (c) (the difference between the 
upper and the lower class limits of each class 
interval) is calculated by the following 
expression: 

Number of class intervals (A:) = Integral part 
of [Range (/?)/Class width (c)] + 1 

NOTE — Integral part means to take only integer value 
and ignore the fraction. It is not advisable to increase 
unnecessarily the number of class intervals so as to 
accommodate one or two extreme observations. Such 
observations can be classified conveniently by making 
first (last) class interval open and this class interval may 
be written as 'less (greater) than or equal to a certain 
value'. 

f) The first class interval is made by taking into 
consideration the minimum value in the data 
and the class width selected above, that is, 
the lower limit of the first class interval should 
be little less than the minimum value and the 
upper limit as the sum of the lower limit 
selected and the class width. For the second 
class interval, the lower limit is taken as the 
upper limit of the first class interval, and the 
class width is added to this to get the upper 
limit of this class interval. In this way the 
subsequent class intervals are also formed. 
The last class interval should contain the 
maximum value in the data. 

g) The class intervals should be defined in such 
a way that each observation belongs to one 
and only one class. This may be achieved by 
specifying class limits to one more decimal 
place than that obtained in the set of 
observations. Alternatively, some arbitrary 
rule can be fixed in advance with regard to 
the allocation of observations coinciding with 
the class limits. This rule shall be speU out 
before summarization is undertaken and 
applied uniformly. 

h) It is desirable to choose the class intervals 
in such a way that the mid-point of the 
intervals is a convenient figure for 
calculation and plotting. Where there is a 
tendency for certain values (for example, 
multiples of 5 or 10) to occur much more 
frequently than the neighbouring values, the 
class intervals should be so arranged that 
these values occur at the middle of the 
corresponding intervals. 

j ) Observations, which are to be grouped, should 
not be rounded off before grouping, 
since grouping is a form of rounding and 



successive rounding is liable to lead to 
systematic errors. 

k) For each observation, as it occurs in the 
original data, a tally mark is put in the suitable 
class interval. For the sake of convenience 
the tally marks are grouped in groups of 5 
each, the fifth tally mark being drawn across 
the other four. When every observation has 
been allotted to a class interval, the tally marks 
in each class interval are counted to get the 
frequency of that class interval. 

m) On a graph paper mark class boundaries on 
A'-axis and frequencies on F-axis. 

n) Make histogram and superimpose the 
specification limits. 

p) Record briefly the source of data and any 
other relevant information on the histogram. 

q) Interpret the histogram for centering, 
variation, shape and process capability. 

7.3 Example 

The data on thickness of 100 metal blocks is given in 
Table 5. The methodology for preparation of frequency 
table and histogram are given in Tabic 6 and Fig. 6 
respectively. 

Table 5 Thickness of Metal Blocks 

Ad dimensions in millimetres. 



3.48 


3.50 


3.42 


3.43 


3.52 


3.49 


3.44 


3.50 


3.50 


3.52 


3.47 


3.48 


3.46 


3.50 


3.56 


3.38 


3.47 


3.49 


3.45 


3.44 


3.50 


3.49 


3.46 


3.46 


3.44 


3.50 


3.45 


3.44 


3.48 


3.46 


3.52 


3.46 


3.32 


3.40 


3.52 


3.34 


3.46 


3.43 


3.30 


3.46 


3.59 


3.47 


3.38 


3.52 


3.45 


3.48 


3.31 


3.46 


3.46 


3.51 


3.48 


3.50 


3.68 


3.60 


3.46 


3.52 


3.56 


3.50 


3.52 


3.46 


3.48 


3.46 


3.52 


3.56 


3.46 


3.45 


3.46 


3.54 


3.54 


3.48 


3.49 


3.41 


3.34 


3.44 


3.47 


3.47 


3.41 


3.48 


3.54 


3.47 


3.56 


3.48 


3.41 


3.55 


3.48 


3.59 


3.40 


3.48 


3.52 


3.41 


3.46 


3.56 


3.37 


3.52 


3.48 


3.63 


3.54 


3.50 


3.48 


3.45 











Range {R) = X^^ - X^^ = 3.68 - 3.30 = 0.38 

Number of Class Intervals (k) = 10 (As per guidelines) 

Class width (c) = 0.38/10 = 0.038 (which is rounded off to 0.05 to 

make class division easier). 

7.4 Uses 

7.4.1 A histogram by displaying the pattern of 
variation, usually communicates information about 
process behaviour and facilitates making decision as 
to where to focus improvement efforts. 

7.4.2 It enables to calculate the mean and the standard 
deviation of the distribution easily. 



IS 15431 : 2003 



Table 6 Frequency Table 

(Clause 7.3) 



SI No. Class 


Mid Frequency Tally 




Fre- 


Boundaries 


Values 




quency 


(1) (2) 


(3) 


(4) 




(5) 


i) 3.275-3.325 


3.30 


/// 




3 


li) 3.325-3.375 


3.35 


/// 




3 


iii) 3.375-3.425 


3.40 


mini 




9 


iv) 3.425 - 3.475 


3.45 


mmm-mmatfii 




32 


IV) 3.475-3.525 


3.50 


mmmimim-mmiii 


38 


V) 3.525-3.575 


3.55 


Jill J J 11 
nttttn 




10 


vi) 3.575-3.625 


3.60 


III 




3 


vii) 3.625-3.675 


3.65 


1 




1 


viii) 3.675-3.725 


3.70 


1 




1 


AH 






















35 ^ 
















30- 




^ 25 






^ 










I 15 






^^^^^ 


^^^^ 








10 - 






^^ 


-JV^fS^ 










5 








r\ 


'Mm^^^^ 


^^^ 


^^^^ 


^^^ 


^^^ 


'^^^ 






in in 

CM fv. 

n oo 


in 

CN 

■<1- 


in in in in 

1^ CN r^ CN 

■<r in m CO 


m 

CO 


in 

CM 

1^ 


CO CO 


7 


CO CO CO CO 


CO 


CO 


m in 

CN CO 


in 

CO 


in in in m 
<N r^ CN r- 
■* ■* in in 


m 

CM 

CO 






CO CO 




CO 


CO 


CO 


CO 


CO 


CO 





Class Intervals — Metal block Thickness (mm) 

Fig. 6 Histogram 

7.4.3 Identification of Problems by the Shape of the 
Distribution 

7.4.3.1 After histogram is prepared, the mid-point of 
each class interval is connected by a smooth curve is 
drawn without following the unevenness of the 
histogram to get a frequency distribution curve. If the 
distribution is normal, this curve usually exhibits a bell- 
like form {see Fig. 7). 




Fig. 7 Frequency Curve 

7.4.3.2 In contrast, non-normal distribution curves 
such as in A-E of Fig. 8 are sometimes obtained. 
Attention shall be paid to the following points in the 
identification of problems on the basis of these 

histograms. 





Fig. 8 Non-normal Distribution Curves 

Curve A: When there is no symmetry, the distribution 
as given in 'A' of Fig. 8 occurs. For example, in the 
distribution of particle size of granules produced by 
grinding, the number of large-size granules decreases 
rapidly while the small size granules exhibit a long- 
tailed distribution. This is because the number of large 
granules is small in the raw material and fine ones occur 
in a natural way even before the grinding operation. 

Curve B: When different types of data are mixed, the 
distribution as given in 'B' of Fig. 8 arises. The shape 
suggests that stratification may be possible operator- 
wise, supplier-wise or instrument-wise. 

Curve C: The distribution as given in 'C of Fig. 8 
often appears when measurements are taken by an 
iiiaccurate method or the class-width is not an integral 
multiple of the measuring unit or any other similar 
factor or cause depending upon the situation. 

Curve D: The distribution as given in 'D' of Fig. 8 
arises when measurements of only those items which 
meet the specifications are recorded or when the 
inspection department makes allowances for sub- 
standard articles to meet the required quantity. It also 
appears when the data below a certain level are 
removed intentionally or when saturation is reached 
in a chemical reaction because there are no data in the 
region beyond the saturation point. 

Curve E: The distribution as given in 'E' of Fig. 8 is 
attributable to differences in quality of raw materials 
or process abnormalities. 

7.4.4 Comparison with Specification and Target Values 

7.4.4.1 When specification limits and target values are 
known, these shall be entered in the histogram and it 
shall be examined whether the actual data distribution 
is satisfactory. The mean should be as close to target 
as possible. 

7.4.4.2 Comparison of the histogram with 
specification limits is explained by taking A-G in 
Fig. 9 as examples. 

Histogram A: The distribution of data is within the 
specification limits with considerable margin on both 
sides. One of the measures is to make the tolerance 



10 



cost or increased productivity can be expected. 

Histogram B: The distribution of data is within the 
specification limits, but the mean (|i) is shifted towards 
the lower specification limit. Therefore, slight decrease 
in the process average may result in off-specification 
items. When this type of distribution appears, steps 
shall be taken to increase the process mean. 

Histogram C: The distribution of data is barely within 
the specification limits. Even a slight change of the 
mean {\x) may produce off-specification items. When 
this type of distribution appears, measures shall be 
taken to reduce the variability of the process or the 
appropriateness of the specification limits shall be 
reviewed. 



appears, action shall be taken immediately. Taking 
into consideration the quality required by the user and 
the capability of the processes, the appropriateness of 
the specification limits shall be reviewed at first. If 
the quality required by the user and the process 
capability can be compromised when the specification 
range is widened to 8 times the standard deviation, 
revision of the specifications is one of the solutions. 
If the shape of the histogram is considerably flat with 
no distinct peak, or like B and C of Fig. 8, the causes 
shall be identified and removed. 

Process improvement may be required if the tolerance 
can be reduced and the distribution is normal. 



iLSL 



USL 



I LSL 



USL 



LSL 



USL 



H 








1 



LSL I 



I „ 

I _ 



dl 



USL 



a. 



LSL ' 



USL 



LSL ' 



jdH 



USL 



d^ 



LSL 



rTI' r4" 



Q 



USL 



Fig. 9 Various Histograms 



11 



IS 15431 : 2003 



Histogram E: The distribution of the data is barely 
within the specification limits, and the mean is shifted 
to the left. This type of distribution may be due to 
three causes: 

a) The items below the lower specification limit 
would not appear under certain manufacturing 
conditions. 

b) The items below the lower specification limit 
might have been eliminated by 100 percent 
inspection. 

c) Off-specification items might have been 
included intentionally within the specification 
limits. This may possibly occur when 
measurement is left to the manufacturing 
department and the rate of off-specification 
items is controlled strictly. 

Action shall be taken to increase the mean to the centre 
of the specification range and reduce the variability of 
the distribution. 

Histogram F: The range of the distribution is smaller 
than that of the specification limits, but data are 
distributed beyond the lower specification limit 
because the midpoint is deviated to the left. Action 
shall be taken to increase the mean. 

Histogram G: Most of the observations are distributed 
within the specification limits and the target value is 
also at the midpoint of the specification range. But 
some observations lie beyond the lower specification 
limit. We have the distribution like E of Fig. 8. As this 
indicates non-normally, the cause shall be detected and 
removed. 

8 STRATIFICATION 

8.1 General 

The idea behind stratification is to differentiate data, 
coming from different sources, as far as possible to 
facilitate tracing back of data indicating problems to 
their origins. Suppose a problem discovered in the 
output of a machine with four spindles, one of which 
is non-conforming items. Merging output from all the 
spindles together will help very little in identifying the 
proper source. However, stratification of data by 
spindles will uncover the problem easily. 

8.2 Scope 

Stratification of data is almost always a prerequisite 
for analysis of data for solving quality problems. Thus 
this exercise is undertaken while using the tools check- 
sheets, cause and effect diagram, Pareto diagram, 
control charts, scatter diagram, sampling, and the like. 

8.3 Steps for Construction 

The steps for construction of stratification may be 
enumerated as follows: 



a) Identify the quality problem to be analyzed 
from Pareto diagram. 

b) Draw a cause-effect diagram. 

c) Classify each quality characteristic by levels 
of one or more factors at a time depending on 
total amount of data and technological 
knowledge of their inter-dependence. Some 
common stratification factors for 
manufacturing applications are: time (day, 
week, month), shift, operators, machines 
(spindles, fixtures, pallets and stations), 
vendors, lots etc. 

d) Design check-sheets suitably for collection of 
data on quality characteristics with 
traceability to the corresponding operational 
level of each factor and its true generation. 

8.4 Uses 

The technique is simple, quick, cheap and yet powerful 
in solving almost all quality problems by identifying 
factors and their levels with favourable and 
unfavourable effects. 

8.5 Examples 

8.5.1 A sample of manufactured product was inspected 
for 6 different types of non-conformity coded as A, B, 
C, D, E and F. The distribution of non-conformities 
according to codes, for the entire output, and 
subsequently stratified by machines are given in 
Table 7. 

Table 7 Distribution of Non-conformities 
According to Non-conformity Codes 

(aaM.ye 8.5.1) 



SI 


Non- 


Number of Non-conformities 


No. 


conformity 


f 




^ 




Code 


Total 


Output of 


Output of 






Output 


Machine 1 


Machine 2 


(I) 


(2) 


(3) 


(4) 


(5) 


i) 


A 


125 


98 


27 


ii) 


B 


55 


12 


43 


iii) 


C 


40 


35 


5 


iv) 


D 


34 


3 


31 


V) 


E 


8 


5 


3 


vi) 


F 


3 


2 


1 




Total 


265 


155 


110 



8.5.2 The Pareto diagram for the total output indicates 
that codes A and B account for about 68 percent of the 
total non-conformities. However, to facilitate taking 
corrective actions, the stratified data by machines 
indicate that for machine 1 non-conformities of type 
A and C (about 86 percent), and for machine 2 non- 
conformities of Type B and D (about 67 percent) 
should be taken care of 

8.5.3 A good many case studies can be cited where 
stratification by men, machine, time, geographical 



12 



IS 15431 : 2003 



locations, vendors, process-stages and the like was 
immensely helpful in pinpointing the source of trouble. 

8.6 Identification of Causes by Stratification 

S.ft.l When the range of distribution is large and the 
rate of off-specification items is high, like D of Fig. 9, 
stratification may be used for the identification of 
causes. The cause that influences the most shall be 
identified and the histogram shall be prepared after 
stratification with respect to the identified cause. When 
stratification with respect to one cause is insufficient, 
it shall be repeated with others. 

8.6.2 Example 1 

There are two peaks in the histogram A in Fig. 1 0. Since 
this histogram is drawn on the basis of observations on 
the products manufactured by two machines, stratification 
by the first and second machine is carried out to obtain 
the two histograms B and C of Fig. 10. 

Stratification reveals that the range of the distribution 
of the product manufactured by the first machine is 
more than that by the second machine and its mean is 
lower. 

8.6.3 Example 2 

The finishing accuracy of a metal roll 200 mm in 
diameter is specified to be under 10/1 000 mm, but 



off-specification articles amounted to 8 percent. The 
first histogram in Fig. 1 1 shows the data of the products 
classified in the classes with the width of 1/1 000 mm. 
This histogram shows apparently that the mean is 
deviated to the left and the tail in extended gradually 
to the right. 

The finishing of the roll was carried out by two 
operators, A and B. Accordingly, two independent 
frequency distribution tables were prepared 
individually for A and B and histogram after 
stratification were prepared as shown in the second 
histogram of Fig. 1 1 . 

In this histogram, the solid line indicates the data of A 
and the dotted line that of B. The number of 
observations for A is 41 and that for B is 109. These 
overlapping histograms show that the products 
manufactured by A are within the specified limits, but 
those by B are widely distributed and B is responsible 
for all the off-specification articles. 

Action must be taken to improve the working accuracy 
of operator B. When the working practice of B was 
examined carefully, it was found that B did not attach 
a roll to the grinder properly. His accuracy improved 
to a large extent when he attached a roll in the same 
way as operator A. 



B 



u 



rd 



£l 



D. 



Original Distribution 



After Stratification by Machine 
No. 1 



After Stratification by Machine 
No. 2 



Fig. 10 Histograms After Stratification by Machines 



Frequency 



Frequency 



^ 



—\ 



H 



Specification 
Value 



hbu 



10x103 10x10^ 

Fig. 1 i Stratified Histograms of Finishing Accuracy of Outside Diameter of Rolls Between Two Operations 



13 



IS 15431 : 2003 



9 RUN CHART 

9.1 General 

A special type of run chart extensively used in statistical 
process control is control chart. A control chart is a 
very useful diagnostic tool for assignable causes of 
variation in a process. Besides, it is used to evaluate 
process capability and to confirm whether process has 
improved after a corrective action has been taken. 

The detailed procedures for construction including 
preliminary steps needed and interpretation of various 
types of control charts have been covered in 
IS 397 (Part 1). 

9.2 Scope 

9.2.1 Besides use as a control chart to understand the 
state (stable or unstable) of a process as indicated 
in 9.1, a run chart can be used to study the nature of 
change over time in any variable of interest to an 
industry, for example, production, consumption of 
energy, customer complaints, profit, machine 
downtime, scrap, productivity, and so on. 

9.3 Steps for Construction 

The steps for drawing a run chart may be enumerated 

as follows: 

a) Identify the variable to be plotted on the run- 
chart, with clearly defined unit of 
measurement. 



b) Decide on the time-points, or time-periods for 
which data are to be plotted. 

c) Scale the jc-axis according to time-points or 
time-periods to be taken. Scale the y-axis 
according to the variable to be plotted. Show 
the zero-point on the ^j-axis, if necessary 
allowing a definite break. 

d) If measurement on a quality characteristic is 
to be plotted (control chart for individual 
items), it is helpful to indicate the target value 
as also the upper and the lower specification 
limits on the chart to facilitate assessment of 
the state of the process. 

e) Observe the variable over time and plot the 
corresponding points on the chart. 

f) Join the successive points by broken lines. 

g) Interpret the chart for trends (upward, 
downward, or more or less static), cycles, shift 
(in a quality characteristic, namely the target 
value and specifications) etc, after a 
sufficiently large number of points are plotted. 

9.4 Examples 

9.4.1 Example of a Run Chart Indicating Trend 

An upward trend is apparent, indicating tool- wear over 
time {see Fig. 12). 



A 



t 



N 

£ 
o 



Time- 



Fig. 12 Run Chart Indicating Trend 



14 



IS 15431 : 2003 



9.4.2 Example Showing Monthly Power Consumption (See Fig. 13) 



t 



Q. 

E 

3 

m 

c 
o 
U 

w 
0) 

o 
a. 




Quarter/Year — ► 

Fig. 13 Run Chart Indicating Power Consumption 

9.4.3 Example Showing Run Chart for Bore-Size of Fly Wheel (Individual Items) (SeeV'ig. 14) 



E 
E. 

0) 
N 

<?5 

0) 

o 
m 




USL 



Target 



LSL 



Sample No. (in the Order of Production) 

Fig. 14 Run Chart for Bore Size of Fly Wheel 



10 SCATTER DIAGRAM 



10.1 General 



The dictionary meaning of the word scatter is sprinkle, 
dissemination or dispersion. In the present context, for 
every quality parameter of interest, there is need to 
assess the nature and/or degree of impact on output of 
resulting 'quality parameter' as reflected in the 
observed changes caused by corresponding variations 
in the 'input parameter'. The former is called 
dependent variable and the latter independent variable. 
Attempts are made to get the behaviour of dependent 
variable in desired range by monitoring the 
independent variable in appropriately determined 
limits as indicated by the nature of relationship between 
the two. The dependent variable is plotted along 



7-axis and the independent along A'-axis. Such a 
diagram is called a scatter diagram. 

10.2 Scope 

10.2.1 Scatter diagrams can be used to establish prima 
facie relationship between output variables reflecting 
quality and input variables, study rejection/rework 
problems, warranty problems etc. 

10.2.2 After a prima facie case of linear or non-linear 
relationship between the variables under study is 
established, from the configuration of points on the 
scatter diagram, further analysis is taken up for 
quantifying the relationship by computing suitable 
numerical measures (correlation, coefficient for linear 
relationship, and correlation index for non-linear 
relationship), and for predicting the dependent variable 



15 



IS 15431 : 2003 



on the basis of the independent one by developing 
suitable regression equations. 

10.2.3 Correlation and regression have been separately 
discussed in IS 7300. 

10.3 Steps for Construction 

The following steps are to be taken for drawing a scatter 
diagram: 

a) Decide on the dependent variable and the 
independent variable whose possible 
relationship is proposed to be studied through 
the scatter diagram. Also decide on the units 
of measurement for each variable. 

b) Scale the A'-axis according to the independent 
variable (X) and the 7-axis according to the 
dependent variable (Y). 

c) Collect data {X, Y) the two variables for a 
sufficiently large number of items (about 50). 

d) Plot these points on the diagram. 

10.4 Example 

Scatter diagram between severed length (effect, output 
variable affecting quality) and conveyor speed (input 
variable) for the data given in Table 8 is shown in Fig. 15. 

Table 8 Data on Conveyor Speed and Severed Length 

{Clause 10.4) 



Convey- 


Severed 


Convey- 


Severed 


Convey- 


Severed 


or Speed 


Length 


or Speed 


Length 


or Speed 


Length 


cni/s 


mm 


cm/s 


mm 


cm/s 


mm 


8.! 


1046 


8.0 


1040 


7.6 


1034 


7.7 


1 030 


5.5 


1 013 


6.5 


1034 


7.4 


1 039 


6.9 


1025 


5.5 


1020 


5.8 


1 027 


7.0 


1 020 


6.0 


1025 


7.6 


1 028 


7.5 


1 022 


5.5 


1023 


6.8 


1025 


6.7 


1020 


7.6 


1028 


7.9 


1 035 


8.1 


1035 


8.6 


1020 


6.3 


1 015 


9.0 


1052 


6.3 


1026 


7.0 


1038 


7.1 


1021 


8.1 


1036 


8.0 


1 036 


7.6 


1024 


6.6 


1023 


8.0 


1026 


8.5 


1029 


6.5 


1011 


8.0 


1 041 


7.5 


1 015 


8.5 


1030 


7.2 


1029 


8.0 


1 030 


7.4 


1014 


6.0 


1 010 


5.2 


1 010 


7.2 


1030 


6.3 


1 020 


6.5 


1025 


5.6 


1016 


6.7 


1024 


8.0 


1031 


6.3 


1020 


8.2 


1 034 


6.9 


1030 







E 1060 

— 1050 

w 1040 

3 1030 

2 1020 i 

I 1010 
CO 



1000 






.♦*♦♦. 



5.0 6.0 7.0 8.0 9.0 

Conveyor Speed (cm/s) 

Fig. 15 Scatter Diagram 



10.0 



10.5 Interpretation 

10.5.1 The configuration of the points on the scatter 
diagram will throw light on the nature of relationship 
between the variables under study. 

10.5.1.1 Linear relationship 

If the points on the scatter diagram lie more or less 
along a straight line, a perfect relationship between 
the variables is indicated (see Fig. 16). 



Fig. 16 Linear Relationship 

10.5.1.2 Positive correlation 

If the line of scatter of the points has a positive slope 
(with an increase in the independent variable, the 
dependent variable also increases on the average), a 
positive correlation is said to exist between the two 
variables and these are said to be positively correlated 
(5eeFig. 17). 



X 
Fig. 17 Positive Correlation 

10.5.1.3 Negative correlation 

If the line of scatter has a negative slope (with an 
increase in the independent variable, the dependent 
variable decreases on an average, and vice versa), a 
negative correlation is said to exist between the 
variables, and these are said to be negatively correlated 
(see Fig. 18). 



X 



Fig. 18 Negative Correlation 



16 



IS 15431 : 2003 



10.5.1.4 No correlation 

If the points do not betray the pattern of a straight line 
(with an increase in the independent variable, there is 
no change, on an average, in the dependent variable), 
there is said to be zero correlation between the 
variables, and these are said to be uncorrelated. Zero 
correlation only means there is no linear relationship 
between the variables. It is possible that there is some 
non-linear relationship {see Fig. 19). 



X 



Fig. 19 No Correlation 



17 



IS 15431 : 2003 



ANNEX A 

{Foreword) 
COMMITTEE COMPOSITION 

Statistical Methods for Quality and Reliability Sectional Committee, MSD 3 



Organization 
Kolkata University, Kolkata 
Bharat Heavy Eiectricals Limited, Hyderabad 

Continental Devices India Ltd, New Deliii 

Directorate General of Quality Assurance, New Delhi 

Laser Science and Technology Centre, DRDO, New Delhi 

Escorts Limited, Faridabad 

HMT Ltd, R&D Centre, Bangalore 

Indian Agricultural Statistics Research Institute, New Delhi 

Indian Association for Productivity, Quality & Reliability, Kolkata 
Indian Institute of Management, Lucknow 
Indian Statistical Institute, Kolkata 

National Institution for Quality and Reliability, New Delhi 

Powergrid Corporation of India Ltd, New Delhi 

SRF Limited, Chennai 



Standardization, Testing and Quality Certification Directorate, 
New Delhi 

Tata Engineering and Locomotive Co Ltd, Jamshedpur 



University of Delhi, Delhi 

In personal capacity (20/1. Krishna Nagar. Safdarjung Enclave. 
New Delhi 110029) 

In personal capacity (B-109, Malviya Nagar.New Delhi 110017) 

BIS Directorate General 



Representative(s) 

Prof S. P. Mukherjee {Chairman) 

Shri S. N. Jha 

Shri a. V. Krjshnan {Alternate) 

Dr Navin Kapur 

Shri Vipul Gupta {Alternate) 

Shri S. K. Srivastva 

Lt Col P. Vijayan {Alternate) 

Dr Ashok Kumar 

Shri C. S. V. Narendra 

Shri K. Vijayamma 

Dr S. D. Sharma 

Dr a. K. Srivastava {Alternate) 

Dr B. Das 

Prof S. Chakraborty 

Prof S. R. Mohan 

Prof Arvind Seth {Alternate) 

Shri Y. K. Bhat 

Shri G. W. Datey {Alternate) 

Dr S. K. Agarwal 

Shr] D. Chakraborty {Alternate) 

Shri A. Sanjeeva Rao 

Shri C. Desigan {Alternate) 

Shri S. K. Kimothi 

Shri P. N. Srikanth {Alternate) 

Shri S. Kumar 

Shri Shanti Sarup {Alternate) 

Prof M. C. Aorawal 
Shri D. R, Sen- 
Prof A. N. Nankana 

Shri P. K. Gambhir, Director and Head (MSD) 
[Representing Director General {Ex-officio)] 



Member Secretary 
Shri Lalit Kumar Mehta 
Joint Director (MSD), BIS 

Panel for Basic Methods Including Terminology, MSD 3:1/P-1 



National Institute for Quality and Reliability, New Delhi 

Laser Science and Technology Centre, DRDO, New Delhi 

Indian Agricultural Statistics Research Institute, New Delhi 

Indian Statistical Institute, New Delhi 

National Institute for Quality and Reliability, New Delhi 

Powergrid Corporation of India Ltd, New Delhi 

In personal capacity {20/1. Krishna Nagar. Safdarjung Enclave, 
New Delhi 110029) 



Shri G. W. Datey {Convener) 

Dr Ashok Kumar 

Dr. S. D. Sharma 

Prof S. R. Mohan 

Shri Y. K. Bhat 

Dr S. K. Agarwal 

Shri D. R. Sen 



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This Indian Standard has been developed from Doc : No. MSD 3 (120). 



Amendments Issued Since Publication 



Amend No. 



Date of Issue 



Text Affected 



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